# How long will a 100Ah battery run an appliance that requires 100W?

In this article, I discuss the amount of time that a 100ah battery could run an appliance that requires 100 watts of power.

As you’ll come to find out after reading this article, this comes down to 2 simple steps:

• Determining the amount of energy (in Watt-hours) that your 100ah is capable of providing on a single charge (Usable Capacity in Wh).
• Determining the amount of energy (in Watt-hours) that your 100w appliance consumes each hour of runtime (Hourly Energy Consumption of the appliance in Wh/hour).

Once you’ve determined these 2 variables, you can use the following formula to calculate the amount of time for which your 100ah battery can run your 100W appliance:

Runtime (hours) = (Usable Capacity of the battery (Wh) ÷ Hourly Energy Consumption of the appliance (Wh/hour)) x 0.85

In this article, I’ll explain these variables and what they represent, and I’ll show you how to determine them. ## How long will a 100ah battery run an appliance that requires 100w?

The amount of time for which a 12V-100ah battery could run a 100W appliance would depend on the type of the battery (chemistry of the battery) and its recommended depth of discharge (DOD), and the amount of energy (in Watt-hours) that the 100W appliance consumes each hour of runtime.

For example, assuming the appliance runs continuously, a 12-volt 100ah lead-acid battery could run a 100w appliance for 4.5 to 5.5 hours at a 50% depth of discharge. On the other hand, a 12V-100ah lithium battery could run the same 100W appliance for 9 to 11 hours at a 100% depth of discharge.

Before I get into what I mean by “a 100w appliance that runs continuously”, an important question to ask is:

If these batteries have the same rated capacity (100ah), why does the lithium battery provide more runtime?

The answer to this question is:

Depth of Discharge (DOD) and Usable Capacity.

let me explain.

Simply put, different battery chemistries have different recommended (or optimal) depths of discharge.

Mainly, we can classify these battery chemistries into two categories:

• Lead-Acid batteries, generally have a recommended depth of discharge of 50%. This means that you can only use 50% of their capacity before they would have to be disconnected or recharged.
• Lithium batteries, generally have a recommended depth of discharge of 80%. Meaning you can only discharge these batteries to 20% of their rated capacity before they’re disconnected and recharged.

If the recommended depth of discharge (DOD) of a battery is exceeded, the battery will sustain irreversible damage (decrease in capacity) and will not last as long as it should (as advertised).

For example, let us assume you have a battery that – at 50% depth of discharge (50% DOD) – is supposed to last 500 charge/discharge cycles before any noticeable decrease in capacity.

If you repeatedly discharge that same battery to a 0% state of charge (100% Depth Of Discharge), you should expect a 30 to 50% decrease in its overall capacity after about 200 charge/discharge cycles.

This means that the amount of energy that you can get out of your 100ah battery does not only depend on its rated capacity (100ah in this case) but also depends on its type or chemistry.

In other words, the actual battery capacity that you can use (hence the term Usable Capacity) before recharging your battery, depends on the rated capacity of your battery, as well as its chemistry and the recommended depth of discharge that comes with that.

So the first variable that needs determining is the Usable Capacity of your battery.

## How much usable capacity does your 100ah battery provide?

As mentioned above, different types of batteries have different recommended depths of discharge (DOD in %).

And these depths of discharge that the manufacturer recommends are usually optimal. Meaning that the manufacturer indicates the best DOD that would result in a good amount of usable capacity, without having that big of a negative impact on the battery.

For example, the following table lists different types of batteries (rated at 100Ah), their recommended depths of discharge (DOD), and their usable capacity based on that DOD:

For example:

let’s consider a 12V-100ah LiFePO4 battery such as the Ampere Time.

Since this is a lithium battery, at an optimal depth of discharge, the usable charge capacity of this battery is 80Ah (Amp-hours).

Now, Amp-hours (Ah) represent Charge Capacity, and what we’re really looking for is the Energy Capacity of the battery in Watt-hours (Wh). To determine the Usable Energy Capacity of our battery, all we have to do is multiply the Usable Charge Capacity (Ah) of the battery by its voltage (V):

Usable Energy Capacity (Watt-hours) = Usable Charge Capacity (Amp-hours) x Battery Voltage (Volts)

The Usable Charge Capacity of our battery is 80Ah and its voltage is 12V. Using our formula, we can calculate the Usable Energy Capacity (Wh) of the battery:

Usable Energy Capacity (Watt-hours) = Usable Charge Capacity (Amp-hours) x Battery Voltage (Volts)

Usable Energy Capacity (Watt-hours) = 80 Ah x 12 V

Usable Energy Capacity (Watt-hours) = 960 Wh

So, according to these calculations, the 12V-100Ah lithium battery from our example can supply 960 Watt-hours of energy before it has to be disconnected or recharged.

For simplicity, we’ll refer to this Usable Energy Capacity as Usable Capacity.

Once you’ve determined the Usable Capacity of your battery, the next step is to determine the hourly energy consumption of your 100W appliance.

## How much energy does the 100W appliance use per hour?

When it comes to appliances, Watts (W) represents the amount of electrical power that the appliance uses when it’s running. And this electrical power represents the rate at which an appliance consumes electrical energy.

The amount of power that an appliance uses when it’s running, along with the amount of time that it ran for (runtime), can both be used to determine the electrical energy that the appliance consumed in this runtime.

The relationship between these 3 variables can be represented as such:

Energy Consumption (Watt-hours) = Power Usage (Watts) x Runtime (hours)

For example, consider a 100W light bulb.

If this light bulb is left on for 1 hour, the amount of electrical energy that it consumes over that hour is:

Energy Consumption (Watt-hours) = Power Usage (Watts) x Runtime (hours)

Energy Consumption (Watt-hours) = 100 Watts x 1 hour

Energy Consumption (Watt-hours) = 100 Watt-hours

However, this only applies to appliances that run continuously (non-stop) when they’re turned on.

Let me explain.

Appliances such as light bulbs, fans, and TVs run continuously. Meaning that when turned on, they stay on and use a steady amount of power (100W for example) until your turn them off.

In this case, you can easily calculate the amount of electrical energy that they would consume each hour based on their rated power (as shown above).

On the other hand, appliances such as refrigerators have what we call a duty cycle. This means that even when turned on, they do not necessarily run 100% of the time, but turn ON and OFF in a way that maintains the set temperature.

For example, a refrigerator will typically only run for about 20-30 minutes per hour. Meaning that if the refrigerator is rated at 100 watts of power, its hourly energy consumption would be around 30-50 Wh/hour.

In any case, once you’ve determined the hourly energy consumption of your 100W appliance, the next and last step is to calculate the amount of time that your 100Ah battery could run the appliance. Using the formula mentioned at the beginning of this article, this should be straightforward:

Runtime (hours) = (Usable Capacity of the battery (Wh) ÷ Hourly Energy Consumption of the appliance (Wh/hour)) x 0.85

Please note that the 0.85 coefficient represents the efficiency of the inverter. (average inverter efficiency is 85%)

Here are 2 examples:

Example 1:

For this example, we’ll assume that we’re trying to run a 100W LED TV on a 12V-100Ah Lead Acid battery.

The first variable here is the usable capacity of the battery. This is a 12V-100Ah Lead Acid battery, which means it has a rated capacity of 1200Wh (Watt-hours).

Since it is Lead Acid, and the recommended depth of discharge for these batteries is typically 50%, we’ll end up with a usable capacity of 600Wh (Watt-hours).

The second variable to determine is the hourly energy consumption of the TV.

As mentioned above, TVs run continuously, and since this is a 100W TV, it will continuously use 100 watts of power:

Hourly Energy Consumption (Watt-hours) = Power Usage (Watts) x 1 hour

Hourly Energy Consumption (Watt-hours) = 100 Watts x 1 hour

Hourly Energy Consumption (Watt-hours) = 100 Watt-hours

So, our usable battery capacity is 600Wh, and our hourly energy consumption is 100Wh/hour. Using our formula, the estimated runtime can be calculated as such:

Runtime (hours) = (Usable Capacity of the battery (Wh) ÷ Hourly Energy Consumption of the appliance (Wh/hour)) x 0.85

Runtime (hours) = (600Wh ÷ 100Wh/hour) x 0.85

Runtime (hours) = (6 hours) x 0.85

Runtime (hours) = 5.1 hours

According to our calculations, our 12V-100Ah Lead Acid battery should be able to run our 100W LED TV for about 5 hours.

Example 2:

For this example, we’ll assume that we’re trying to run a 100W fridge on a 12V-100Ah Lithium battery.

The first variable here is the usable capacity of the battery. This is a 12V-100Ah Lithium battery, which means it has a rated capacity of 1200Wh (Watt-hours).

Since it is Lithium, and the recommended depth of discharge for these batteries is typically 80%, we’ll end up with a usable capacity of 960Wh (Watt-hours).

The second variable to determine is the hourly energy consumption of the fridge.

Assuming the ambient temperatures are not extreme, and as a general rule of thumb, our 100W fridge will only really run for about 20 minutes each hour (0.33 hours). Its hourly energy consumption could be estimated as such:

Hourly Energy Consumption (Watt-hours) = Power Usage (Watts) x 0.33 hours

Hourly Energy Consumption (Watt-hours) = 100 Watts x 0.33 hours

Hourly Energy Consumption (Watt-hours) = 33 Watt-hours

So, our usable battery capacity is 960Wh, and our hourly energy consumption is 33 Wh/hour. Using our formula, the estimated runtime can be calculated as such:

Runtime (hours) = (Usable Capacity of the battery (Wh) ÷ Hourly Energy Consumption of the appliance (Wh/hour)) x 0.85

Runtime (hours) = (960Wh ÷ 33Wh/hour) x 0.85

Runtime (hours) = (29 hours) x 0.85

Runtime (hours) = 24.7 hours

According to our calculations, our 12V-100Ah Lithium battery should be able to run our 100W fridge for about 24 hours, give or take.

The last thing to keep in mind is that you would also need an inverter.

Make sure the inverter is rated for 12V nominal Input Voltage. As per the power rating of the inverter, in this particular case, a 500W to 1000W continuous power rating would be a good fit. 